The river model of black holes

This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. %that can by understood by non-experts. In the river model, space itself flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. We show that the river model works also for rotating (Kerr-Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, the river has at each point not only a velocity but also a rotation, or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation), not just three (velocity). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point, and that encapsulates all the properties of a stationary rotating black hole.Comment: 16 pages, 4 figures. The introduction now refers to the paper of Unruh (1981) and the extensive work on analog black holes that it spawned. Thanks to many readers for feedback that called attention to our omissions. Submitted to the American Journal of Physic

Phosphorus and arsenic distributions in a seasonally-stratified, iron- and manganese-rich lake: microbiological and geochemical controls

Seasonal stratification in temperate lakes greater than a few metres deep provides conditions amenable to pronounced vertical zonation of redox chemistry. Such changes are particularly evident in eutrophic systems where high phytoplankton biomass often leads to seasonally-established anoxic hypolimnia and profound changes in geochemical conditions. In this study, we investigated the behaviour of trace elements in the water column of a seasonally-stratified, eutrophic lake. Two consecutive years of data from Lake Ngapouri, North Island, New Zealand, demonstrate the occurrence of highly correlated profiles of phosphorus (P), arsenic (As), iron (Fe) and manganese (Mn), all of which increased in concentration by 1-2 orders of magnitude within the anoxic hypolimnion. Stoichiometric and mass-balance considerations demonstrate that increases in alkalinity in hypolimnetic waters were consistent with observed changes in sulfate, Fe and Mn concentrations with depth, corresponding to dissimilatory reduction of sulfate, Fe(III) and Mn(IV) hydroxides. Thermodynamic constraints on Fe, Mn and Al solubility indicate that amorphous Fe(III), Mn(IV) hydroxides most probably controlled Fe and Mn in the surface mixed layer (~0 to 8 m) while Al(III) hydroxides were supersaturated throughout the entire system. Surface complexation modelling indicated that iron hydroxides (HFO) potentially dominated As speciation in the lake. It is likely that other colloidal phases such as allophanic clays also limited HPO42- activity, reducing competition for HAsO42- adsorption to iron hydroxides. This research highlights the coupling of P, As, Fe and Mn in Lake Ngapouri, and the apparent role of multiple colloidal phases in affecting P and As activity within overarching microbiological and geochemical processes

A high resolution UV absorption spectrum of supernova ejecta in SN1006

We report a high resolution, far-ultraviolet, STIS E140M spectrum of the strong, broad Si II, III, and IV features produced by the ejecta of SN1006 seen in absorption against the background Schweizer-Middleditch star. The spectrum confirms the extreme sharpness of the red edge of the redshifted Si II 1260 A feature, supporting the idea that this edge represents the location of the reverse shock moving into the freely expanding ejecta. The expansion velocity of ejecta at the reverse shock is measured to be 7026 +-3(relative) +-10(absolute) km/s. If the shock model is correct, then the expansion velocity should be decreasing at the observable rate of 2.7 +-0.1 km/s per year. The pre-shock velocity, post-shock velocity, and post-shock velocity dispersion are all measured from the Si II 1260 A feature, and consistency of these velocities with the shock jump conditions implies that there is little or no electron heating in this fast (2680 km/s) Si-rich shock.Comment: 9 pages, 5 embedded postscript fig

Emergent Critical Phase and Ricci Flow in a 2D Frustrated Heisenberg Model

We introduce a two-dimensional frustrated Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. Classically the two sublattices decouple, and "order from disorder" drives them into a coplanar state. Applying Friedan's geometric approach to nonlinear sigma models, we show that the scaling of the spin-stiffnesses corresponds to the Ricci flow of a 4D metric tensor. At low temperatures, the relative phase between the spins on the two sublattices is described by a six-state clock model with an emergent critical phase.Comment: 4+ pages, 2 figure

Mass inflation in a D dimensional Reissner-Nordstrom black hole: a hierarchy of particle accelerators ?

We study the geometry inside the event horizon of perturbed D dimensional Reissner-Nordstrom-(A)dS type black holes showing that, similarly to the four dimensional case, mass inflation also occurs for D>4. First, using the homogeneous approximation, we show that an increase of the number of spatial dimensions contributes to a steeper variation of the metric coefficients with the areal radius and that the phenomenon is insensitive to the cosmological constant in leading order. Then, using the code reported in arXiv:0904.2669 [gr-qc] adapted to D dimensions, we perform fully non-linear numerical simulations. We perturb the black hole with a compact pulse adapting the pulse amplitude such that the relative variation of the black hole mass is the same in all dimensions, and determine how the black hole interior evolves under the perturbation. We qualitatively confirm that the phenomenon is similar to four dimensions as well as the behaviour observed in the homogeneous approximation. We speculate about the formation of black holes inside black holes triggered by mass inflation, and about possible consequences of this scenario.Comment: 8 pages, 6 figure

Increasing Microcystis cell density enhances microcystin synthesis: a mesocosm study

An experimental protocol using mesocosms was established to study the effect of Microcystis sp. cell abundance on microcystin production. The mesocosms (55 L) were set up in a shallow eutrophic lake and received either no (control), low (to simulate a moderate surface accumulation), or high (to simulate a dense surface scum) concentrations of Microcystis sp. cells collected from the lake water adjacent to the mesocosms. In the low- and high-cell addition mesocosms (2 replicates of each), the initial addition of Microcystis sp. cells doubled the starting cell abundance from 500 000 to 1 000 000 cells mL⁻¹, but there was no detectable effect on microcystin quotas. Two further cell additions were made to the high-cell addition mesocosms after 60 and 120 min, increasing densities to 2 900 000 and 7 000 000 cells mL-1, respectively. Both additions resulted in marked increases in microcystin quotas from 0.1 pg cell-1 to 0.60 and 1.38 pg cell⁻¹, respectively, over the 240 min period. Extracellular microcystins accounted for <12% of the total microcystin load throughout the whole experiment. The results of this study indicate a relationship between Microcystis cell abundance and/or mutually correlated environmental parameters and microcystin synthesis

Comment on "Canonical formalism for Lagrangians with nonlocality of finite extent"

We show by some counterexamples that Lagrangian sysytems with nonlocality of finite extent are not necessarily unstable.Comment: 8 pages, 1 figure Submitted to Phys. Rev.

Hindcasting cyanobacterial communities in Lake Okaro with germination experiments and genetic analyses

Cyanobacterial blooms are becoming increasingly prevalent worldwide. Sparse historic phytoplankton records often result in uncertainty as to whether bloom-forming species have always been present and are proliferating in response to eutrophication or climate change, or if there has been a succession of new arrivals through recent history. This study evaluated the relative efficacies of germination experiments and automated rRNA intergenic spacer analysis (ARISA) assays in identifying cyanobacteria in a sediment core and thus reconstructing the historical composition of cyanobacterial communities. A core (360 mm in depth) was taken in the central, undisturbed basin of Lake Okaro, New Zealand, a lake with a rapid advance of eutrophication and increasing cyanobacteria populations. The core incorporated a tephra from an 1886 volcanic eruption that served to delineate recent sediment deposition. ARISA and germination experiments successfully detected akinete-forming nostocaleans in sediment dating 120 bp and showed little change in Nostocales species structure over this time scale. Species that had not previously been documented in the lake were identified including Aphanizomenon issatschenkoi, a potent anatoxin-a producer. The historic composition of Chrococcales and Oscillatoriales was more difficult to reconstruct, potentially due to the relatively rapid degradation of vegetative cells within sediment

Separating E and B types of polarization on an incomplete sky

Detection of magnetic-type ($B$-type) polarization in the Cosmic Microwave Background (CMB) radiation plays a crucial role in probing the relic gravitational wave (RGW) background. In this paper, we propose a new method to deconstruct a polarization map on an incomplete sky in real space into purely electric and magnetic polarization type maps, ${\mathcal{E}}(\hat{\gamma})$ and ${\mathcal{B}}(\hat{\gamma})$, respectively. The main properties of our approach are as follows: Firstly, the fields ${\mathcal{E}}(\hat{\gamma})$ and ${\mathcal{B}}(\hat{\gamma})$ are constructed in real space with a minimal loss of information. This loss of information arises due to the removal of a narrow edge of the constructed map in order to remove various numerical errors, including those arising from finite pixel size. Secondly, this method is fast and can be efficiently applied to high resolution maps due to the use of the fast spherical harmonics transformation. Thirdly, the constructed fields, ${\mathcal{E}}(\hat{\gamma})$ and ${\mathcal{B}}(\hat{\gamma})$, are scalar fields. For this reason various techniques developed to deal with temperature anisotropy maps can be directly applied to analyze these fields. As a concrete example, we construct and analyze an unbiased estimator for the power spectrum of the $B$-mode of polarization $C_{\ell}^{BB}$. Basing our results on the performance of this estimator, we discuss the RGW detection ability of two future ground-based CMB experiments, QUIET and POLARBEAR.Comment: 43 pages, 15 figures, 1 table. The finial version, will appear in PR

The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries